Question

Question #91037

Answer 1

This can be the area of a square, and when `x=5`, the area of the square is `64`.

Explanation:

In order for this expression to be the area of a square, the quadratic would have to be a perfect square.

Factoring out the quadratic would give:
`9x^2-42x+49=(3x-7)^2`

Since the quadratic factors out to be a perfect square, any value of `x` would result in a perfect square. Thus, this can be the area of a square.

In order for the area of the square to be `64\text{m}^2` , we can just equate the two expressions:
`(3x-7)^2=64`

Simplifying gives:
`3x-7=8`
`3x=15`
`x=5`